On interpretation of recent proper motion data for the Large Magellanic Cloud

Recent observational studies using the Hubble Space Telescope (HST) have derived the center-of-mass proper motion (CMPM) of the Large Magellanic Cloud (LMC). Although these studies carefully treated both rotation and perspective effects in deriving the proper motion for each of the sampled fields, they did not consider the effects of local random motion in the derivation. This means that the average PM of the fields (i.e., the observed CMPM) could significantly deviate from the true CMPM, because the effect of local random motion can not be close to zero in making the average PM for the small number of the fields (~10). We discuss how significantly the observationally derived CMPM can deviate from the true CMPM by applying the same method as used in the observations for a dynamical model of the LMC with a known true CMPM. We find that the deviation can be as large as ~ 50 km/s (~0.21 mas/yr), if the LMC has a thick disk and a maximum circular velocity of ~120$ km/s. We also find that the deviation depends both on the total number of the sampled fields and on structure and kinematics of the LMC. We therefore suggest that there is a possibility that the observed CMPM of the LMC deviates from the true one to some extent. We also show that a simple mean of PM for a large number of the LMC fields (~1000) can be much closer to the true CMPM.